Israel bombarded dozens of targets in the Gaza Strip on Tuesday, stepping up what it said might become a long-term offensive against Islamist Hamas after a surge in Palestinian rocket attacks on Israeli towns.

Following the worst outbreak of violence along the Gaza frontier since an eight-day war in 2012, the Israeli military said a ground invasion of the enclave was possible, though not imminent, and urged citizens within a range of 40 km of the coastal territory to stay close to bomb shelters.

"We are preparing for a battle against Hamas which will not end within a few days," Defence Minister Moshe Yaalon said in a statement.

"We will not tolerate missiles being fired at Israeli towns and we are prepared to extend the operations with all means at our disposal in order to keep hitting Hamas."

A source in Prime Minister Benjamin Netanyahu's office quoted the Israeli leader as saying: "The IDF (Israel Defense Forces) must be ready to go all the way. All options are on the table, including a ground invasion."

The Israel-Gaza border heated up last month after Israel's arrest of hundreds of Hamas activists in the occupied West Bank, where three Israeli youths went missing on June 12.

More than 200 rockets have been launched at Israel from the Gaza Strip, the military said, since Israel mounted the dragnet while searching for the teens, who were found dead last week.

Israel has accused Hamas militants of killing them. In a suspected revenge attack, a Palestinian teen was abducted in East Jerusalem last Wednesday. His charred body was found in a forest and six Israeli suspects have been arrested.

In the Gaza fighting, a Hamas fighter was killed in an air strike in Nusseirat refugee camp, Palestinian medical officials said. Palestinian officials said targets included militants' training facilities while six homes were bombed in the Gaza Strip and 30 people were also wounded.

The Israeli military said that in the past 24 hours, more than 100 rockets had been fired at Israel, a sharp increase. Some were intercepted by the Iron Dome anti-missile system, but two people were wounded by shrapnel.

Some 1,500 Israeli reservists had been mobilised and more could be called up, the military said.

Explosions echoed across the Gaza Strip on Tuesday, shaking buildings and sending smoke rising from targets hit by Israeli fire. In residential areas, the sounds of crying children could be heard as ambulance sirens wailed. Some people took to rooftops to watch for Israeli aircraft and rockets streaking toward Israel.

In the Israeli port city of Ashdod, motorists scrambled out of their vehicles and raced for the relative safety of apartment house entrances as a siren sounded. The scene was repeated in other towns near the Gaza Strip.

Hamas' armed wing, the dominant force in the enclave, threatened an "earthquake" in response to Israel's attacks. But a Palestinian source close to the group said it was ready to restore calm if Israel met conditions, including a prisoner release. The Israeli military, announcing it had launched "Operation Protective Edge", said it targeted about 50 sites in aerial and naval assaults overnight and resumed air strikes on Tuesday morning after rockets were fired at southern Israeli towns.

Warning sirens, which police described as false alarms, sounding as far away as Tel Aviv and Jerusalem, some 70 km from Gaza.

The heavy barrage followed the deaths, in disputed circumstances on Monday, of six Hamas men in a tunnel which the Israeli military said the militant group had built under the border to carry out an attack in Israel.

In one Israeli attack overnight that destroyed a Gaza home, the Palestinian Interior Ministry said the family received a telephone call from an Israeli officer telling them to leave. But the ministry said nine neighbours were wounded.

At least one of the targeted homes belonged to a Hamas militant, according to a neighbour.

Setting out terms for a truce, the source close to Hamas said Israel had to "stop all forms of aggression", recommit to a 2012 Egyptian-brokered ceasefire and release prisoners it detained in the occupied West Bank last month.

Hamas has been reeling over an Egyptian crackdown on most of the estimated 1,200 cross-border smuggling tunnels run by the group, which Egypt says are used to take weapons into the Sinai Peninsula.

A further weakening of Hamas could lead to more radical Islamist groups in Gaza becoming stronger, a scenario that could alarm Israel.-Reuters